Rational functions are not very useful for obtaining global differential models because they involve poles that may eject the trajectory to infinity. In contrast, it is here shown that they allow one to significantly improve the quality of models for maps. In such a case, the presence of poles does not involve any numerical difficulty when the models are iterated. The models then take advantage of the ability of rational functions to capture complicated structures that may be generated by maps. The method is applied to experimental data from copper electrodissolution.